Embed Size (px)
Citation preview
www.justmaths.co.uk Version 2 November 2015
Forming & Solving Equations A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas.
1. Kieran, Jermaine and Chris play football.
• Kieran has scored 8 more goals than Chris.
• Jermaine has scored 5 more goals than Kieran.
• Altogether they have scored 72 goals.
How many goals did they each score?
Kieran ............................
Jermaine ............................
Chris ............................
[5]
2. In this row of boxes, you start with 5 and 7.
You add 5 and 7 to get 12 to go in the third box.
You add 7 and 12 to get 19 to go in the fourth box.
You add 12 and 19 to get 31 to go in the fifth box.
Complete these rows of boxes using the rule shown above.
(a)
[1]
Name:
Total Marks:
www.justmaths.co.uk Version 2 November 2015
(b)
[2]
(c) Complete this row of boxes, writing your expressions in their simplest form.
[2]
(d) Use your answer to (c) to help you fill in the missing numbers in this row of
boxes.
[3]
3. The perimeter of the triangle is the same length as the perimeter of the square.
Find an expression for the length of one side of the square in terms of a.
Give your answer in its simplest form.
.............................. [4]
www.justmaths.co.uk Version 2 November 2015
4. Here is a pentagon.
Write down an expression for the perimeter of the pentagon.
Give your answer in its simplest form.
..................................................... [1]
5. Shape A is a rectangle of length x cm and width 2 cm.
The shape below contains two rectangles that are identical to shape A.
Work out an expression for the perimeter of this shape.
Give your answer in its simplest form.
............................................... cm [3]
www.justmaths.co.uk Version 2 November 2015
6. This is a square.
Work out the length of the side of the square.
.................................................... cm [5]
7. ABCH is a square.
HCFG is a rectangle.
CDEF is a square.
www.justmaths.co.uk Version 2 November 2015
They are joined to make an L-shape.
Show that the total area of the L-shape, in cm2, is x 2 + 9x + 27
[4]
8. Here is a parallelogram.
Work out the value of x and the value of y.
x = ...........................................................
y = ...........................................................
[5]
9. Rob buys p packets of plain crisps and c packets of cheese crisps.
Write down an expression for the total number of packets of crisps Rob buys.
.......................................................
[1]
www.justmaths.co.uk Version 2 November 2015
10. Here is a rectangle made of card.
The measurements in the diagram are in centimetres.
Lily fits four of these rectangles together to make a frame.
The perimeter of the inside of the frame is P cm.
(a) Show that P = 8x – 4y
[2]
Magda says,
“When x and y are whole numbers, P is always a multiple of 4.”
(b) Is Magda correct?
You must give a reason for your answer.
.......................................................................................................................
...................................................................................................................[2]
11. Dimitar has 20 sweets.
Pip also has 20 sweets.
Dimitar gives Pip x sweets.
Dimitar then eats 5 of his sweets.
Pip then eats half of her sweets.
www.justmaths.co.uk Version 2 November 2015
Write expressions for the number of sweets Dimitar and Pip now have.
Dimitar ................................. Pip ................................. [3]
12. You can use this rule to work out the total cost, in pounds, of hiring a carpet
cleaner.
Andy hires a carpet cleaner.
The total cost is £82.20
(a) Work out the number of days Andy hires the carpet cleaner for.
.......................................................days [2]
Chloe hires a carpet cleaner for y days.
The total cost is £T.
(b) Write down a formula for T in terms of y.
....................................................... [2]
13. In the diagram all measurements are in centimetres.
www.justmaths.co.uk Version 2 November 2015
The perimeter of the quadrilateral is twice the perimeter of the triangle.
Work out the perimeter of the quadrilateral.
....................................................... cm [4]
14. Write an expression for the total cost, in pounds, of
x jumpers at £15 each
and
y shirts at £12 each.
[1]
15. Three boxes contain counters.
There are 62 counters in total.
The total number of counters in box A and box B is 34
The difference between the number of counters in box A and box C is 9
Work out the number of counters in each box.
Box A ______ Box B ______ Box C ______ [3]
16. A shape is made from rectangles.
(a) On the diagram below shade an area represented by the expression ab
[1]
www.justmaths.co.uk Version 2 November 2015
(b) On the diagram below shade an area represented by the expression ad + cd
[1]
(c) On the diagram below shade the area represented by the expression d(a + 2c)
[1]
(d) Write down an expression for the area of the whole shape.
[1]
www.justmaths.co.uk Version 2 November 2015
17. Three straight lines are shown.
Work out the value of x.
[3]
18. Which of these can be written as 𝑎
𝑏 ?
Circle your answer.
[1]
b ÷ a a – b a ÷ b b – a
19. The diagram shows a square.
Work out the length of one side of the square.
[4]
www.justmaths.co.uk Version 2 November 2015
20. Each diagram represents a balance with the total weight on each side being
equal.
Find the values of A, B and C.
A = ………………………kg B = ………………………kg C = ………………………kg [3]
21. Charlie has x pens.
Lisa has 3 more pens than Charlie.
Julian has twice as many pens as Lisa.
How many pens do Charlie, Lisa and Julian have altogether?
Simplify your answer as far as possible.
[4]
www.justmaths.co.uk Version 2 November 2015
22. The diagram shows a square.
All the lengths are measured in centimetres.
Diagram not drawn to scale
Use an algebraic method to find the length of one side of the square.
[5]
23. The diagram shows a right-angled triangle.
All the angles are in degrees.
Work out the size of the smallest angle of the triangle.
[3]
www.justmaths.co.uk Version 2 November 2015
24. ABCD is a trapezium.
A square has the same perimeter as this trapezium.
Work out the area of the square.
Give your answer correct to 3 significant figures.
...................................................... cm2 [5]
www.justmaths.co.uk Version 2 November 2015
CREDITS AND NOTES
Question Awarding Body Question Awarding Body
1 OCR 13 Pearson Edexcel
2 OCR 14 AQA
3 OCR 15 AQA
4 OCR 16 AQA
5 OCR 17 AQA
6 OCR 18 AQA
7 AQA 19 AQA
8 Pearson Edexcel 20 WJEC Eduqas
9 Pearson Edexcel 21 WJEC Eduqas
10 Pearson Edexcel 22 WJEC Eduqas
11 Pearson Edexcel 23 Pearson Edexcel
12 Pearson Edexcel 24 Pearson Edexcel
Notes:
These questions have been retyped from the original sample/specimen
assessment materials and whilst every effort has been made to ensure there
are no errors, any that do appear are mine and not the exam board s (similarly
any errors I have corrected from the originals are also my corrections and not
theirs!).
Please also note that the layout in terms of fonts, answer lines and space given
to each question does not reflect the actual papers to save space.
These questions have been collated by me as the basis for a GCSE working
party set up by the GLOW maths hub - if you want to get involved please get
in touch. The objective is to provide support to fellow teachers and to give you
a flavour of how different topics “could” be examined. They should not be used
to form a decision as to which board to use. There is no guarantee that a topic
will or won’t appear in the “live” papers from a specific exam board or that
examination of a topic will be as shown in these questions.
Links:
AQA http://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300
OCR http://ocr.org.uk/gcsemaths
Pearson Edexcel http://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html
WJEC Eduqas http://www.eduqas.co.uk/qualifications/mathematics/gcse/
Contents:
This version contains questions from:
AQA – Sample Assessment Material and Practice set 1
OCR – Sample Assessment Material and Practice set 1
Pearson Edexcel – Sample Assessment Material, Specimen set 1 and Specimen set 2.
WJEC Eduqas – Sample Assessment Material
